Question

5. A type of elevator has a maximum weight capacity Yi, which is normally distributed with mean 5,000 pounds and standard deviation 300 pounds. For a certain building equipped with this type of elevator, the elevator's load, Y2, is a normally distributed random variable with mean 4,000 pounds and standard deviation 400 pounds. For any given time that the elevator is in use, find the probability that it will be overloaded assuming n and Y2 are independent

Answer 1

here let difference between capacity in load A=Y1-Y2

mean of A =E(Y1-Y2)=E(Y1)-E(Y2)=5000-4000=1000

and std deviation of A =sqrt(Var(Y1-Y2))=sqrt(Var(Y1)+Var(Y2))=sqrt(300²+400²)=500

therefore P(elevator will be overloaded)=P(A<0)=P(Z<(0-1000)/500)=P(Z<-2)=0.0228